Game Theory Week 2 Quiz Answers
Game Theory Week 2 Quiz Answers
In this article i am go to share Coursera Course Game Theory Week 2 Quiz Answers with you..
Week 2 Quiz Answers
Question 1)
Find a mixed strategy Nash equilibrium where player 1 randomizes over the pure strategy Left and Right with probability pp for Left. What is pp?
- 1/2
- 2/3
- 1/4
- 3/4
Question 2)
In a mixed strategy Nash equilibrium where player 1 plays Left with probability pp and player 2 plays Left with probability qq. How do pp and qq change as XX is increased (X>1X>1)?
- p is the same, q decreases.
- p increases, q increases.
- p decreases, q decreases.
- p is the same, q increases.
Question 3)
- There are 2 firms, each advertising an available job opening.
- Firms offer different wages: Firm 1 offers w_1=4w1=4 and 2 offers w_2=6w2=6.
- There are two unemployed workers looking for jobs. They simultaneously apply to either of the firms.
- If only one worker applies to a firm, then he/she gets the job
- If both workers apply to the same firm, the firm hires a worker at random and the other worker remains unemployed (and receives a payoff of 0).
Find a mixed strategy Nash Equilibrium where pp is the probability that worker 1 applies to firm 1 and qq is the probability that worker 2 applies to firm 1.
- p=q=1/4p=q=1/4;
- p=q=1/2p=q=1/2;
- p=q=1/5p=q=1/5.
- p=q=1/3p=q=1/3;
Question 4)
- A king is deciding where to hide his treasure, while a pirate is deciding where to look for the treasure.
- The payoff to the king from successfully hiding the treasure is 5 and from having it found is 2.
- The payoff to the pirate from finding the treasure is 9 and from not finding it is 4.
- The king can hide it in location X, Y or Z.
Suppose the pirate has two pure strategies: inspect both X and Y (they are close together), or just inspect Z (it is far away). Find a mixed strategy Nash equilibrium where pp is the probability the treasure is hidden in X or Y and 1-p1−p that it is hidden in Z (treat the king as having two strategies) and qq is the probability that the pirate inspects X and Y:
- p=4/9p=4/9, q=2/5q=2/5;
- p=1/2p=1/2, q=1/2q=1/2;
- p=5/9p=5/9, q=3/5q=3/5;
- p=2/5p=2/5, q=4/9q=4/9;
Question 5)
- A king is deciding where to hide his treasure, while a pirate is deciding where to look for the treasure.
- The payoff to the king from successfully hiding the treasure is 5 and from having it found is 2.
- The payoff to the pirate from finding the treasure is 9 and from not finding it is 4.
- The king can hide it in location X, Y or Z.
Suppose that the pirate can investigate any two locations, so has three pure strategies: inspect XY or YZ or XZ. Find a mixed strategy Nash equilibrium where the king mixes over three locations (X, Y, Z) and the pirate mixes over (XY, YZ, XZ). The following probabilities (king), (pirate) form an equilibrium:
- (1/3, 1/3, 1/3), (4/9, 4/9, 1/9);
- (1/3, 1/3, 1/3), (1/3, 1/3, 1/3);
- (4/9, 4/9, 1/9), (1/3, 1/3, 1/3);
- (1/3, 1/3, 1/3), (2/5, 2/5, 1/5);